Minimum Rényi and Wehrl entropies at the output of bosonic channels
Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone, Jeffrey H. Shapiro, Brent J. Yen · Physical Review A · 2004
The minimum R\'enyi and Wehrl output entropies are found for bosonic channels in which the signal photons are either randomly displaced by a Gaussian distribution (classical-noise channel), or coupled to a thermal environment through lossy propagation (thermal-noise channel). It is shown that the R\'enyi output entropies of integer orders $z\ensuremath{\geqslant}2$ and the Wehrl output entropy are minimized when the channel input is a coherent state.